This book deals with the numerical analysis and efficient numerical
treatment of high-dimensional integrals using sparse grids and
other dimension-wise integration techniques with applications to
finance and insurance. The book focuses on providing insights into
the interplay between coordinate transformations, effective
dimensions and the convergence behaviour of sparse grid methods.
The techniques, derivations and algorithms are illustrated by many
examples, figures and code segments. Numerical experiments with
applications from finance and insurance show that the approaches
presented in this book can be faster and more accurate than
(quasi-) Monte Carlo methods, even for integrands with hundreds of
dimensions.
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